1-7
PART 2
Midpoint and Distance
in the Coordinate Plane
Vocabulary
Review
1. A right triangle contains one angle that measures
.
Complete each statement with hypotenuse or leg.
2. The longest side of a right triangle is the 9.
3. In a right triangle, each of the sides that form the right angle is a 9.
4. Circle the right triangle.
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Vocabulary Builder
distance (noun, verb)
DIS
tuns
Related Word: distant (adjective)
Main Idea: Distance is a measurement of length. Distance is measured in units
such as inches, feet, centimeters, and meters.
Definition: Distance is the amount of space between two objects, locations, points,
lines, or figures.
Use Your Vocabulary
Determine whether the word distance is used as a noun or a verb in each sentence.
Circle the correct choice.
5. Seven miles is a distance too great to walk in one hour.
noun / verb
6. He tries to distance himself from other runners in the race.
noun / verb
7. I see a mountain in the distance.
noun / verb
55
Lesson 1-7, Part 2
Key Concept The Distance Formula
The distance between two points A(x1, y1) and B(x2, y2) is d 5 "(x2 2 x1) 2 1 (y2 2 y1) 2 .
The Distance Formula is based on the Pythagorean Theorem.
y
B
y2
y1
d
c
A
a
x2 x1
O
b
y2 y1
x1
a2
x
b2 c2
x2
Use the diagrams above. Draw a line from each triangle side in Column A to the
corresponding triangle side in Column B.
Column A
Column B
17. y2 2 y1
a
18. x2 2 x1
b
19. distance, d
c
Problem 3 Finding Distance
y
S(–2, 14)
Got It? SR has endpoints S(22, 14) and
20. Complete the diagram at the right.
8
21 2 14 5
4
21. Let S(22, 14) be (x1, y1) and let
R(3, 21) be (x2, y2) . Use the
justifications and complete the
steps below to find SR.
x
Ľ8
Ľ4
3 2 (22) 5
d5
SR 5
5
5
5
<
Chapter 1
Ä
Ä
Ä
Ä
Ä
Q
2 x1 R 2 1 Q
Q
2 (22) R 2 1 Q
Q
R2 1 Q
1
R2
2 y1 R 2
2 14 R 2
6
R(3, –1)
Use the Distance Formula.
Substitute.
Subtract.
Simplify powers.
Add.
Use a calculator and round to the nearest tenth.
56
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R(3, 21). What is SR to the nearest tenth?
Problem 4 Finding Distance
Got It? On a zip-line course, you are harnessed to a cable that travels through the
treetops. You start at Platform A and zip to each of the other platforms. How far do
you travel from Platform D to Platform E? Each grid unit represents 5 m.
2200
A
C
30
30
30
50
D
y
F
10
10
10
10
10 O
10
10
20
20
30
30
40
40
x
50
10
10
10
E
20
220
0
B
22. The equation is solved below. Write a justification for each step.
d 5 "(x2 2 x1) 2 1 (y2 2 y1) 2
DE 5 "(30 2 20) 2 1 (215 2 20) 2
5 "102 1 (235) 2 5 "100 1 1225 5 "1325
23. To the nearest tenth, you travel about
m.
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Lesson Check • Do you UNDERSTAND?
Reasoning How does the Distance Formula ensure that the distance between two
different points is positive?
24. A radical symbol with no sign in front of it indicates a positive / negative square root.
25. Now answer the question.
__________________________________________________________________________________
Math Success
Check off the vocabulary words that you understand.
midpoint
distance
coordinate plane
Rate how well you can use the Midpoint and Distance Formulas.
Need to
review
0
2
4
6
8
Now I
get it!
10
57
Lesson 1-7, Part 2